Susan, hong, and juan sent a total of 107 text messages over their cell phones during the weekend. hong sent 4 times as many messages as juan. juan sent 5 fewer messages than susan. how many messages did they each send?

susan sent 22 texts

Hong sent 68 texts

Juan sent 17 texts

Step-by-step explanation:

Let x represent the number of text messages that Susan sent during the weekend.

Let y represent the number of text messages that Hong sent during the weekend.

Let z represent the number of text messages that Juan sent during the weekend.

Susan, Hong, and Juan sent a total of 107 text messages over their cell phones during the weekend. This means that

x + y + z = 107 - - - - - - - - 1

Hong sent 4 times as many messages as Juan. This means that

y = 4z

Juan sent 5 fewer messages than Susan. This means that

x = z + 5

Substituting y = 4z and x = z + 5 into equation 1, it becomes

z + 5 + 4z + z = 107

z + 4z + z = 107 - 5

6z= 102

z = 102/6 = 17

x = z + 5 = 17 + 5 = 22

y = 4z = 17×4 = 68